6 papers
Free Skew Braces and Free Solutions of the Yang--Baxter Equation
Eric Jespers, Thomas Letourmy, Silvia Properzi +2
We offer a workable construction of the free right nilpotent skew braces of arbitrary class which allows us to prove (among many other things) that this free object has free additi…
On Dehornoy's representation for the Yang-Baxter equation
Carsten Dietzel, Edouard Feingesicht, Silvia Properzi
This article investigates Dehornoy's monomial representations for structure groups and Coxeter-like groups associated with a set-theoretic solution to the Yang--Baxter equation. Us…
Finiteness conditions on skew braces and solutions of the Yang-Baxter equation
Rosa Cascella, Silvia Properzi, Arne Van Antwerpen
A finite non-degenerate set-theoretic solution of the Yang-Baxter equation gives rise to a structure skew brace that is a -skew brace, i.e. every element has…
L-algebras and their ideals: from simplicity to semidirect products
Silvia Properzi, Yufei Qin
In this paper, we investigate the ideals of semidirect products of L-algebras and the structure of simple L-algebras. We provide a precise characterization of the ideals of semidir…
Common divisor graphs for skew braces
Silvia Properzi, Arne Van Antwerpen
We introduce two common divisor graphs associated with a finite skew brace, based on its - and -orbits. We prove that the number of connected components is at most two and…
Indecomposable involutive set-theoretical solutions to the Yang-Baxter equation of size
Carsten Dietzel, Silvia Properzi, Senne Trappeniers
The quantum Yang-Baxter equation is a braiding condition on vector spaces which is of high relevance in several fields of mathematics, such as knot theory and quantum group theory.…